The Value of Everything But the Cost of Nothing

1
The Value of Everything But the Cost of Nothing

• A Tutorial to Haskell

Shu-Chun "scw" Weng scw _AT_ csie _DOT_
org http//scw.tw/works/OSDCtw2007/slides.ppt
2
Whats The Title?

• One of the famous epigrams in programming by Alan
  J. Perlis, the first recipient of the Turing
  Award.
• One man's constant is another man's variable.
• In English every word can be verbed. Would that
  it were so in our programming languages.
• Origins from LISP programmers.

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Outline

• Why Haskell?
• What's Haskell?
• Syntax
• Sample code

4
Why Haskell?

• http//haskell.org

They are all open source software!
5
Why Haskell?

• Pugs
• Implementation of Perl 6
• darcs
• Distributed, interactive, smart RCS
• lambdabot
• GHC

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Why Haskell?

• Powered by Ph.D.!
• http//haskell.org/haskellwiki/Research_papers

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Why Haskell?
From freenode, perl6, 2005/3/2
http//xrl.us/e98m 1908 Does pugs
yet have system() or backticks or qx// or any way
to use system
commands? 1908 malaire no, but I
can do one for you now. a sec 1909
ok, I'm still reading YAHT, so I won't try to
patch pugs just yet... 1909 you want
unary system or list system? 1909
system("ls -l") vs system("ls", "-l") 1910 malaire perhaps list, but either is ok 1911 autrijus \\n Bool pre system
(Str)\ 1911 \\n Bool pre
system (Str List)\ 1911 I'll do
both ) 1911 done. testing. 1914 autrijus test passed. r386. enjoy 1914 malaire that's quite fast development ) 1914 autrijus )
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Whats Haskell?

• Functional programming language
• A Style of programming
• A language that Supports and Encourages it
• Specific WHAT to do, not HOW to do.
• Pure
• No assignment, no side effect
• Less bug!
• No more Segmentation fault 11 (core dumped)
• map f . map g map (f . g)
• f(x) f(x) 2 f(x)
• Mutable variables eliminated from .NET by Bill
  Taylor on 2007/04/01

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Whats Haskell?

• Higher order functions
• Functions are also value
• takeWhile isAlpha only the first word
• greaterThan n \x - x n
• Lazy
• 1 ..
• primes sieve 2 ..
• sieve (pxs) p sieve x x 0

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Whats Haskell?
(Rice U.) Walid Taha Why do you
put type annotations all over your
functions?" Under grad. student They make the
code more readable and the interface
explicit." Walid Taha Well,
they're too verbose, and you really should be
able to tell
the types easily by looking at them. And you
should also
learn how to deal with those type error
messages. (Yale U.) Paul Hudak Stating the
types explicitly is considered good coding
style." Paul Hudak You should annotate all your
functions with types."

• Strongly typed
• No type casting, no runtime type check
• Except unsafeCoerce or unsafePerformIO
• No union
• But there is Either Int Double
• Sometimes too hypercritical, but it pays
• Type inference
• Dont have to maintain the type of variable
  ourself
• Still can provide type-signature
• For double check
• Explicit interfacing

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Whats Haskell?

• Haskell 98 Language Report on 03
• QuickSort
• QuickSort (xxs) QuickSort y y y x

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How to Run Haskell

• Get GHC from http//haskell.org/ghc/
• ghc Main.hs
• Main.hi
• Main.c
• a.out or Main.exe
• ghci Main.hsPrelude Main QuickSort 9, 4, 1,
  2, 61,2,4,6,9

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Goal

• Write a Haskell program to solve following puzzle
• Find paths in a n by n by n cube
• From one corner block to the furthest one
• Visit every block exactly once (Hamilton path)
• 8-connected, i.e. each stop to neighbor block
• One path? All paths? Number of paths?

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Syntax

• Representing coordinates and paths
• Pair (tuple)
• (1, 1, 2)
• fst (a, b) a snd (a, b) b
• List
• R, U, L, F, R, D, L
• Cons 1 2, 3 1, 2, 3
• head 1, 2, 3 1 tail 1, 2, 3 2, 3
• 1, 2, 3 4, 5, 6 1, 2, 3, 4, 5, 6
• O, S, D, C OSDC

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Syntax

• Functions on lists
• 4, 5, 6 !! 2 5
• take 3 7, 8, 9, 10, 11, 12 7, 8, 9
• map (3) 1, 2, 3 4, 5, 6
• filter isAlpha a1 b2 c3 abc
• map uc osdc OSDC
• zip 1, 2, 3, 4, 5 2, 4, 8, 16, 32
  (1, 2), (2, 4), (3, 8), (4, 16), (5, 32)
• fiblist 0 1 zipWith () fiblist (tail
  fiblist)

WHAT THE FK ARE YOU WRITING?
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Syntax

• Mathematician writes function as f(x)
• Haskell guys write it f x
• Reserve parentheses for ordering
• lisp is full of parentheses, please dont do so
  in Haskell
• Mathematicians write f(g(x))
• lisp programmers write (f (g x))
• Haskell guys write it f (g x)
• Or, clearer, f g x
• f(x, g(y)) f x g y

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Syntax

• Functions on lists
• 4, 5, 6 !! 2 5
• take 3 7, 8, 9, 10, 11, 12 7, 8, 9
• map (3) 1, 2, 3 4, 5, 6
• filter isAlpha a1 b2 c3 abc
• map uc osdc OSDC
• zip 1, 2, 3, 4, 5 2, 4, 8, 16, 32
  (1, 2), (2, 4), (3, 8), (4, 16), (5, 32)
• fiblist 0 1 zipWith () fiblist (tail
  fiblist)

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Syntax

• Mathematicians also write f(g(x)) as (f?g)(x)
• Its troublesome to key in ?, thus we use (f .
  g) x
• cflowizeProgram cflowize () .
  cflowOptimizeProgram . guarding ()
• doCompile doCflow chainExpand .
  (if doCflow then cflowizeProgram else id) .
  third . third . tiMain2 .
  (if doCflow then cflowDesugarProgram else id)
• main interact (unlines . map reverse . lines)
  -- command rev on Unix system

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Syntax

• How about write an ad-hoc function?
• ? in the lambda-calculus
• Written as \x - x
• map (\x - 3 x) 1, 2, 3 4, 5, 6
• is a infix operator but we usually write
  functions in prefix
• () is prefix () 1 2 1 2 3
• f is infix 3 elem 2, 3, 4
• \x - 3 x \x - () 3 x () 3 (3)

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Syntax

• Variable declaration? let it! Or define by
  where.
• let size 3 count size size size -
  1 start (1, 1, 1) finish (size,
  size, size) in searching code
• test_in_range (x, y, z) bounded x
  bounded y bounded z where bounded n n
  0 n
• Note the indentation!

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Syntax

• Control flow
• No goto of course
• if then else
• Always have else part since we are defining
  functions
• case of - -
• if b then do_this else do_that case b of
  True - do_this False - do_that

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Syntax

• Loop

There is no loop! Recursive, please!

• int sum(int n, int list) int s 0
  for(int i 0 i return s
• sum 0sum (xxs) x sum xs
• sum foldr () 0

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Syntax

• Strongly typed but didnt see any type yet!
• Thanks to type inference ?
• Built-in types
• Int, Double, Char, String Char
• (Int, Int, Int), (Char, Double)
• Function type Int - Int - Int
• Int - (Int - Int)
• Polymorphic type a b. (a, b) - a

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Syntax

• Type synonym
• type Cursor (Int, Int, Int)
• type Trail Set Cursor
• type State (Move, Cursor, Trail)
• Algebraic datatypes
• data Move L R U D F A
  deriving Show
• chooses L, R, U, D, F, A

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Syntax

• Polymorphic? Isnt it template/generic?
• fst (a, b) a fst (a, b) - a
• head (xxs) x head a - a
• Cannot manipulate generic data!
• Except that data is in some class
• toString Show a a - StringtoString x
  ( show x )
• Function show provided by class Show
• class Show t where show t - String

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Syntax

• How to tell the world that our move can be
  shown?
• Instance it!
• data Move deriving Show
• instance Show Move where show L L
  show R R

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Syntax

• Ok, weve told the world that our move can be
  shown, but how to really tell the world?
• I/O is terrible in traditional functional
  language! non-pure
• Monad!
• putStr String - IO ( )
• print Show a a - IO ( )

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Syntax

• Monad is MORE than IO
• Maybe, Error, Continuation
• List
• single_step State - State
• single_step states do (path, cursor, trail)
  next

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Sample Code

• single_step State - State
• single_step states do (path, cursor, trail)
  next nextpath new_cursor move_cursor
  cursor next new_trail Set.insert
  new_cursor trail guard (test_in_range
  new_cursor) guard (test_no_collision
  new_cursor trail) return (new_path,
  new_cursor, new_trail)

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Sample Code

• Move cursor? Pattern matching!
• move_cursor Cursor - Move -
  Cursormove_cursor (x, y, z) L (x1, y,
  z)move_cursor (x, y, z) R (x-1, y,
  z)move_cursor (x, y, z) U (x, y1,
  z)move_cursor (x, y, z) D (x, y-1,
  z)move_cursor (x, y, z) F (x, y,
  z1)move_cursor (x, y, z) A (x, y, z-1)

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Sample Code

• Ready to derive the solution?
• solutions Movesolutions map
  keep_path foldr () initial all_steps
  where initial (, start, Set.singleton
  start)
• all_steps replicate count
  single_step keep_path (path, _, _)
  path
• Fold!
• foldr f z x1, x2, ..., xn x1 f (x2 f ...
  (xn f z)...)
• replicate Int - a - a

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Sample Code

• main IO ()
• Print all solutions
• main mapM_ print solutions
• Print one solution
• main print head solutions
• Print number of solutions
• main print length solutions
• http//scw.tw/works/OSDCtw2007/Main.hs

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Further Reading

• YAHT http//en.wikibooks.org/wiki/Haskell/YAHT
• All about monadhttp//www.haskell.org/all_about_m
  onads/html/index.html
• The Essence of Functional Programming
  http//homepages.inf.ed.ac.uk/wadler/papers/essenc
  e/essence.ps
• irc.freenode.org haskell
• GHC libraryhttp//www.haskell.org/ghc/docs/latest
  /html/libraries/index.html

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Q?
35
Thanks !

• ?

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Performance

• Vanilla sieve
• primes sieve 2 ..
• sieve (pxs) p sieve x x 0
• Less tests
• primes sieve 2 ..
• sieve (pxs) p sieve x x notFactorIn primes
  squares x
• noFactorIn (pps) (qqs) x q
  x x mod p 0 noFactorIn ps qs x
• squares p p p
• 66 faster for P100, 90 for P1000, 94 for P5000